1. Field of the Invention
This invention relates to a narrow band acoustic source, and a method for constructing and using said source.
2. Description of the Related Art
High frequency acoustic sources have been used to obtain good resolution of geologic features during logging operations. Conventional acoustic sources used in well logging generate signals having frequencies in the range of 5 kHZ to 25 kHz. These sources provide vertical resolution of features on the order of 2-5 ft. (0.6 m-1.5 m). However, penetration of the surrounding formation is severely limited, reaching only approximately 10 feet (3 m) beyond the borehole in which the source is located. The conventional sources thus cannot be used for cross-hole imaging. For cross-hole imaging low frequency signals are usually employed. However, low frequency signals, say, on the order of 100 Hz, do not provide good resolution of features smaller than 20-50 feet. They do however, provide excellent penetration.
One of the limitations on penetration is signal bandwidth. The relationship of the amplitude of the signal at the central frequency, A(.omega..sub.o) to the total power of the device, P.sub.T and the bandwidth of the signal, 2.pi..GAMMA. is shown in Equation (1): EQU .vertline.A(.omega..sub.o).vertline..sup.2 =P.sub.T /2.pi..GAMMA.Eq. (1)
The total power, P.sub.T, is fixed by the instrumentation and power supply system. Therefore, as bandwidth increases, amplitude decreases. By narrowing the bandwidth, greater amplitude and thus penetration into the formation should be possible. For example reduction in bandwidth from say 10 kHz to 5 Hz, a factor of 2000, would provide an increase of signal level by a factor of (2000).sup.1/2 .apprxeq.45 at a finite .GAMMA..
Crosswell signal levels fall roughly as R.sup.-2 in our experience where R is the range. Thus, we could increase our range by a factor of (45).sup.-2 .apprxeq.6.7 relative to conventional crosshole devices operating in broadband mode.